calculate the number of best fit golden rectangles in a given area

Hello all :-)

Here's an interesting one that is not as simple as it seems at first.

Lets say my daughter has a piece of paper. It has a height (H) and width (W).

She wants to draw an arial view of a number of farmers fields (N). The thing is she's been learning about the golden ratio in art, and wants all of the fields such that they are Golden Rectangles. All of the fields are the same size and have the width (A) and Length (B). She also wants a gap (G) between the fields so the farmer can walk around them without getting amongst the crops and livestock. She also wants the same gap around the perimeter of the farm plot.

The question is this. For a given number of fields (N), what is the formula to calculate the individual field length (B) and width (A) expressed in terms of the Gap (G), paper height (H) and paper width (W) assuming that all fields are Golden Rectangles, and that there is also a gap equal to (G) all the way round the perimeter of the farm?

Have fun

DK

Approved by CB

Re: calculate the number of best fit golden rectangles in a given area

Quote:

Originally Posted by

**daviskites** Hello all :-)

Here's an interesting one that is not as simple as it seems at first.

Lets say my daughter has a piece of paper. It has a height (H) and width (W).

She wants to draw an arial view of a number of farmers fields (N). The thing is she's been learning about the golden ratio in art, and wants all of the fields such that they are Golden Rectangles. All of the fields are the same size and have the width (A) and Length (B). She also wants a gap (G) between the fields so the farmer can walk around them without getting amongst the crops and livestock. She also wants the same gap around the perimeter of the farm plot.

The question is this. For a given number of fields (N), what is the formula to calculate the individual field length (B) and width (A) expressed in terms of the Gap (G), paper height (H) and paper width (W) assuming that all fields are Golden Rectangles, and that there is also a gap equal to (G) all the way round the perimeter of the farm?

Have fun

DK

Is this a problem for which you want a solution or a challenge to other members of MHF?

CB

Re: calculate the number of best fit golden rectangles in a given area

It's a problem I was pondering, and came up with a near solution. So I guess it's a challenge. I am new to the forum - are challenges OK?

Thank you

DK

Re: calculate the number of best fit golden rectangles in a given area

Quote:

Originally Posted by

**daviskites** It's a problem I was pondering, and came up with a near solution. So I guess it's a challenge. I am new to the forum - are challenges OK?

Thank you

DK

They should go in the challenges area, but first you should seek approval from the moderators before posting them there.

CB

Re: calculate the number of best fit golden rectangles in a given area

came up with a near solution.

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